Spatial resolution and dissipation rate estimation in Taylor--Couette flow for tomographic PIV

Abstract

This paper assesses the spatial resolution and accuracy of tomographic particle image velocimetry (PIV). In tomographic PIV the number of velocity vectors are of the order of the number of reconstructed particle images, and sometimes even exceeds this number when a high overlap fraction between adjacent interrogations is used. This raises the question of the actual spatial resolution of tomographic PIV in relation to the various flow scales. We use a Taylor-Couette flow of a fluid between two inde- pendently rotating cylinders and consider three flow regimes: laminar flow, Taylor vortex flow and fully tur- bulent flow. The laminar flow has no flow structures, and the measurement results are used to assess the measure- ment uncertainty and to validate the accuracy of the tech- nique for measurements through the curved wall. In the Taylor vortex flow regime, the flow contains large-scale flow structures that are much larger than the size of the interrogation volumes and are fully resolved. The turbulent flow regime contains a range of flow scales. Measurements in the turbulent flow regime are carried out for a Reynolds number Re between 3,800 and 47,000. We use the mea- sured torque on the cylinders to obtain an independent estimate of the energy dissipation rate and estimate of the Kolmogorov length scale. The data obtained by tomo- graphic PIV are assessed by estimating the dissipation rate and comparing the result against the dissipation rate obtained from the measured torque. The turbulent flow data are evaluated for different sizes of the interrogation vol- umes and for different overlap ratios between adjacent interrogation locations. The results indicate that the tur- bulent flow measurements for the lowest Re could be (nearly) fully resolved. At the highest Re only a small fraction of the dissipation rate is resolved, still a reasonable estimate of the total dissipation rate could be obtained by means of using a sub-grid turbulence model. The resolution of tomographic PIV in these measurements is determined by the size of the interrogation volume. We propose a range of vector spacing for fully resolving the turbulent flow scales. It is noted that the use of a high overlap ratio, that is, 75 %, yields a substantial improvement for the estimation of the dissipation rate in comparison with data for 0 and 50 % overlap. This indicates that additional information on small-scale velocity gradients can be obtained by reducing the data spacing.